The Robust Maximum Principle

Both refining and extending previous publications by the authors, the material in this monograph has been class-tested in mathematical institutions throughout the world. Covering some of the key areas of optimal control theory (OCT)¿a rapidly expanding field that has developed to analyze the optimal behavior of a constrained process over time¿the authors use new methods to set out a version of OCT¿s more refined ¿maximum principle¿ designed to solve the problem of constructing optimal control strategies for uncertain systems where some parameters are unknown. Known as a ¿min-max¿ problem, this type of difficulty occurs frequently when dealing with finite uncertain sets. The text begins with a standalone section that reviews classical optimal control theory. Moving on to examine the tent method in detail, the book then presents its core material, which is a more robust maximum principle for both deterministic and stochastic systems. The results obtained have applications in production planning, reinsurance-dividend management, multi-model sliding mode control, and multi-model differential games. Using powerful new tools in optimal control theory, this book explores material that will be of great interest to post-graduate students, researchers, and practitioners in applied mathematics and engineering, particularly in the area of systems and control.